A further note on the P.N.T. error term
A further omega result for the ellipsoid problem in algebraic number fields
A further refinement of Mordell's bound on exponential sums
A fuzzy commitment scheme with McEliece's cipher.
A Gauss-Bonnet theorem for motivic cohomology.
A Gauss-Kuzmin theorem for the Rosen fractions
Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.
A Gauss-Kuzmin-Lévy theorem for a certain continued fraction.
A Gel'fond type criterion in degree two
A general arithmetic construction of transcendental non-Liouville normal numbers from rational fractions
A general class of sieve generated sequences
A general discrepancy estimate based on p-adic arithmetics
A general framework for subexponential discrete logarithm algorithms
A general notion of independence of sequences of integers.
A generalisation of an identity of Lehmer
We prove an identity involving generalised Euler-Briggs constants, Euler's constant, and linear forms in logarithms of algebraic numbers. This generalises and gives an alternative proof of an identity of Lehmer (1975). Further, this identity facilitates the investigation of the (conjectural) transcendental nature of generalised Euler-Briggs constants. Earlier investigations of similar type by the present authors involved the interplay between additive and multiplicative characters. This in turn...
A generalisation of Artin's conjecture for primitive roots
A generalisation of Mahler measure and its application in algebraic dynamical systems
We prove a generalisation of the entropy formula for certain algebraic -actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.
A generalization of a necessary and sufficient condition for primality due to Vantieghem.
A generalization of a problem of Chebyshev
A generalization of a result of André-Jeannin concerning summation of reciprocals.
A generalization of a result of Fermat.